Analogues of Entire Function Inequalities for an Analytic Function

Abstract

1. Let be an analytic function with radius of convergence R (0 < R < ∞). Setand let the order p and lower order ⋋ of f(z) be defined bywhere x = Rr/(R — r). If 0 < ᑭ < ∞, we define the type T and lower type t of f(z) byAlso, if 0 < ᑭ < ∞, define the “growth numbers” 𝛄 and δ byThe purpose of our discussion will be to obtain some inequalities involving the growth constants defined above.